This is merely the ontological argument inappropriately applied to science. What proof do you have that empiricism exists solely in the mind? The fact that you are comparing the so called circular logic of science to the circular logic of the bible is a balance fallacy: the "circular logic" of science has been proven time and time again whereas the circular logic of the bible is, by definition, circular and cannot be proven therefore the two do not merit the same level of scrutiny or debate. Raising the logic of the bible to the same level as the logic of science (circular logic versus proven logic) implies that if science is false then the bible must be true.
This matter has nothing to do with the ontologcal argument, it is a matter of epistemic foundation and internal consistency. At the bottom of the creationist worldview is the Bible. At the bottom of the metaphysical naturalist world view is reason. There exists no justification for reason in metaphysical naturalism, it is just a brute fact that is accepted essentially on faith and justified in purely pragmatic terms. I know of no deductive argument that justifies reason as a foundation for metaphysical naturalism that is not question begging. Just as you can't use the Bible to justify the Bible you can't use reason to justify reason. Using reason to justify reason -- which is what you are implicitly doing -- is just as circular and self-referential as using the Bible to justify the Bible.
The Young Earth Creationist worldview is just as internally consistent as the metaphysical naturalist worldview that you are appealing to. External incosistency can't be use as an argument against a another worldview because that amounts to the arbitrary privileging of one worldview over another. Yes, YEC is externally incosistent with matephysical naturalism but so what?
EDIT: Additionally, not all science is gathered from empiricism. A good deal of it are derived from mathematical proofs and concepts which cannot be experienced in the way that empiricism describes and also flow in an entirely logical manner. In fact, most of the empirical evidence we have (like for example the observation that gravity causes two masses to accelerate to each other) can be mathematically verified and could have been verified without any observation.
You are correct that not all of science is based on empricism, in practoce it is based on a blend of rationalism and empricism and this manifests itself in the use of inductive logic and deductive logic. However you are mistaken about the relationship between mathematics and the physical world. Only those that believe in Platonic realism subscribe to your belief. (Also it can be argued that Platonic realism is inconsistent with metaphysical naturalism.) Mathematical concepts aren't "out there" floating in space waiting to be discovered. They are human artifacts. Applied mathematics is able to describe the physical world because it was designed (by humans) to do that. The physical world exhibits an ordered regularity and we invent mathematical concepts to facilitate the description of that regularity and the final equations are described as laws. The physical world doesn't have "laws of physics" in it, it just has regluar behaviour. Mathematics is a descriptive and analytical language that we invented and develop to aid our description of the world. There are no such things as imaginary numbers and complex numbers, they were invented because they enable use to model certain aspects of the physical world. Broadly speaking it is no more remarkable that there as verbs to describe actions than there are equations to describe (and predict) physical phenomena.
I refer you to my above response. But, just in case you decide not to read it or you missed it or something I will reiterate it.
First, what is metaphysical naturalism. Metaphysics is a pseudoscience and naturalism is the study of nature. What they mean together is anyone's guess.
Second, science is not reason justified by reason. Science is
observation (italicized to emphasis my point) put together into mathematical or verbal models which are then put together into the highest level of science known as theories. For example, the observation that in any chemical reaction, matter and energy are neither created nor destroyed has led to the law of conservation of mass and the law of conservation of energy. This, in turn, contributes to many theories such as quantum theory. Where, in this flow, is there reason being used to justify reason. All I see is observation being explained. The bible, on the other hand, flows like this:The bible is infallible. It is infallible because it is the word of God. The bible says the word of God is infallible. Repeat.
Thirdly, give me an alternate view of the many laws which near as hell perfectly describe the real world? P = mv (momentum) F = ma (force) V = IR (voltage, current, resistance). The real world does have laws, that is what makes the real world different than a fantasy novel. The laws can be, and have been, demonstrated over and over again.
Fourthly, what is the difference between what you call ordered regularity and what the rest of the world calls the laws of physics.
Fifthly, when have the laws of physics as we know them today ever been falsified?
Sixthly, your attempt at a gish gallop is quite juvenile.
Finally, you have never addressed my question of giving me a specific example (just one will do) of science basing reason on reason